I have been working in Boston for the past 6 months on an every other week basis, our main location for stays have been in an around Copley Square with our office 2 blocks off of Fenway Park. I generally search Google Maps, locate restaurants and then read reviews (sorting by most recent, no most relevant). Have not visited as many down by Custom House but here are a few highlights:
By Custom House
Bostonia Public House - fun, young crowd - very busy for Happy Hour. Enjoyed the NE Clam Chowder and a Lobster Roll
Trillium - this is a brewery and one of the top MA locations. The food on the second floor is very well prepared and beer is outstanding. Be certain to get a reservation as I don't believe they serve any food on the main floor of brewery
North End - only went to one location but as noted above - reservations and most any place would be great
By Copley Square (we generally walk to locations, better weather longer walks):
Lolita's - hip Mexican location with goth theme. Very good food, just not long on value (2 tacos for $16)
Buttermilk and Bourbon - hip southern cooking / small plate. The biscuits (also not cheap) are heavenly and the chicken thighs are so good
Post 390 - very good food, main floor more tavern like, upstairs is finer dining
Summer Shack - very good seafood location in a unique location (above a bowling alley). very good crab cake sandwich
Lobstah on a Roll - as the name says - small hole in the wall location, mostly to go but a few chairs to sit
5 Horses Tavern - South End - fun tavern with pizza, burgers tacos, etc. also a good beer tap list if interested
Back Bay Social - ok location with varied menu
Whiskey's - think college town sports bar
Earl's - Canadian chain restaurant in Prudential Center - good food and fun, energized crowd
The Gallow's - interesting small location, good burgers
Coda - another small restaurant with very good food
Salty Pig - unique pizza's and a few pastas, fun atmosphere
Brownstone - generally good food - they have a foccacia appetizer that looks amazing
Around Town
Cava - think Chipotle, but Mediteranian food (very good, eat here for lunch at least 1 time per week)
Sweet Greens - think Chipotle, but with salads - not one of our favorites
Tasty Burger - good greasy burger and fries
Yet to Try:
Stoked - pizza west of Fenway (also have a food truck)
The Smoke Shop BBQ - multiple locations, believe was on Diner's, Drive-Ins and Dives